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Double-flat alternatives in comparison
In the old discussions mentioned in some of the answers, Abraham proposed a
compromise that kept the original glyph width by applying an average
compression to both flats.
I've used MetaFont's proof sheets (with outlines so show how the flat
symbols are put together on the left and the filled-in normal versions to
check the visual appearance).
There has been some manual cleansing of distracting outlines of superimposed
parts and I've unified some parameters that made the counter (the small
"hole" in the flat symbol) look slightly different in some accidentals
containing flats.
1. Original Feta design
The compressed left flat even "bites off" part of the lower stem and makes
it look considerably thinner. And the compression of the left flat only
reminds me of a rear-shunt car crash, sort of... ;)
<http://lilypond.1069038.n5.nabble.com/file/t3887/double-flat-1-original.png>
2. Abraham's equally compressed flats
Both flats are equally compressed as a compromise, thus keeping the original
glyph width:
<http://lilypond.1069038.n5.nabble.com/file/t3887/double-flat-2-abraham-equal.png>
3. Torsten's "real" flats with maximum overlap
Both flats are "real" unaltered flats. Maximum overlap makes the double-flat
glyph only marginally wider than the original design (cf. Dorico's Bravura
font):
<http://lilypond.1069038.n5.nabble.com/file/t3887/double-flat-3-torsten-real-overlap.png>
4. Abraham's "real" flats with minimum overlap
Both flats are "real" unaltered flats, there is only a slight overlap. This
is the widest of all the designs mentioned here (cf. Sibelius' Opus font):
<http://lilypond.1069038.n5.nabble.com/file/t3887/double-flat-4-abraham-real.png>
All the graphics have exactly the same height/width and glyph positioning,
so you can download them and flip through them to directly see how the
design slightly changes from image to image and gradually widens up.
What do you think?

I would vote for changing the current design, i.e. rule out version 1)
I don't really like the compressed version 2)

If I had to choose between 3) and 4) I would go for 4), but actually I'd
suggest to go for something between those two.
The problem with 4) is obviously (and only) that it takes much
horizontal space - especially if you extend it to triple flats.
The problem I have with 3) is the upper edge of the intersection between
the left and right glyph: I have the impression (although this should be
verified in a realistic-sized setting with notational context) that this
section is somewhat blurred because the line is still nearly horizontal
at the intersection.